The tensor Harish-Chandra-Itzykson-Zuber integral

• Verfasst von: Collins, Benoît [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Lionni, Luca [VerfasserIn]
• Titel: The tensor Harish-Chandra-Itzykson-Zuber integral
• Titelzusatz: I. Weingarten calculus and a generalization of monotone Hurwitz numbers
• Verf.angabe: Benoît Collins, Razvan Gurau, Luca Lionni
• Ausgabe: Version v2
• E-Jahr: 2022
• Jahr: 25 Jan 2022
• Jahr des Originals: 2020
• Umfang: 43 S.
• Fussnoten: Version 1 vom 26. Oktober 2020, Version 2 vom 25. Januar 2022 ; Gesehen am 05.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: (2020), Artikel-ID 2010.13661, Seite 1-43
• DOI: doi:10.48550/arXiv.2010.13661
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematical Physics
• Sach-SW: Mathematics - Combinatorics
• K10plus-PPN: 1804433136

Abstract

We study a generalization of the Harish-Chandra - Itzykson - Zuber integral to tensors and its expansion over trace-invariants of the two external tensors. This gives rise to natural generalizations of monotone double Hurwitz numbers, which count certain families of constellations. We find an expression of these numbers in terms of monotone simple Hurwitz numbers, thereby also providing expressions for monotone double Hurwitz numbers of arbitrary genus in terms of the single ones. We give an interpretation of the different combinatorial quantities at play in terms of enumeration of nodal surfaces. In particular, our generalization of Hurwitz numbers is shown to enumerate certain isomorphism classes of branched coverings of a bouquet of $D$ 2-spheres that touch at one common non-branch node.